In electronics a NOT gate is more commonly called an inverter. The circle on the symbol is called a bubble, and is used in logic diagrams to indicate a logic negation between the external logic state and the internal logic state (1 to 0 or vice versa).
A weather watch, on the other hand, typically refers to an alert issued to indicate that conditions are favorable for the development of dangerous weather patterns, although the dangerous weather conditions themselves are not currently present.
Each segment of the HWO will contain 3 sections: short term through Day 1, long term for Days 2-7, and spotter information. Winter Storm Watch. A Winter Storm Watch is issued when there is the potential for significant and hazardous winter weather within 48 hours.